Chapter 4 — Calculation Method¶

(This section was marked "to be added" in the printed Fifth Edition manual. The summary below is drawn from Chapter 1 and from the behavior of the current GATB release.)

Overview of the GATB Calculation Pipeline¶

GATB is a graphical HVE front-end for the ATB (Articulated Total Body) rigid-body dynamics program (this version is based upon ATB-V.1, June 1998). The calculation proceeds as follows:

Data extraction — GATB extracts the human, vehicle, environment and event data from HVE and writes a complete ATB input file (gatb.ain), automatically selecting the appropriate ATB options, card images (A-, B-, C-, D-, F- and H-cards), contact panels, belt/harness and airbag data.
ATB solution — The embedded ATB solver integrates the equations of motion of the 15-segment, 14-joint articulated body. Segment-vs-panel, segment-vs-segment, belt and airbag forces are evaluated each time step. GATB always uses a fixed ATB integration time step of 0.002 sec, which it writes into the time-step field of the A4 card; the number of steps is the maximum simulation time divided by 0.002. The other values on the A4 card (.00050, .00100, .0000625) are ATB minimum-time-step and print/integration-control fields — the .00050 is not a "human-collision" step. Within each step the integration is handled by the variable-step Runge-Kutta/predictor-corrector integrator internal to ATB.
Output return — The solver's standard output (gatb.aou), structured output (.sal) and time-history (tape 8) files are read back and converted into the HVE reports described in Chapter 3 (Accident History, Human Data, Injury Data, Program Data, Results, Vehicle Data, Variable Output and Trajectory Simulation).

The human model is the HVE human data set: 15 mass segments, each with up to 3 contact ellipsoids, connected by 14 joints (up to 4 joints attach to a single segment). Injury measures (HIC, HSI, CSI) are computed by the ATB post-processor.

What GATB computes, and what ATB computes¶

The division is worth being explicit about, because it determines where to look when a result is questioned.

ATB computes all of the physics: the equations of motion of the articulated body, the joint models, the segment-versus-panel and segment-versus-segment contact forces, and the harness and airbag models. None of that is GATB's, and none of it is described in this manual — see the CVS/ATB documentation.

GATB computes the translation from HVE's data model into ATB's. Most of that translation is a direct transfer of a value from one place to another, with unit conversion where the two differ — ATB takes angles in degrees, for instance, where HVE stores them in radians. A few quantities, however, are genuinely constructed by GATB, and those are given below because they are not recoverable from either program's documentation alone.

Contact panels¶

An HVE contact surface is stored as three corner points. ATB expects a panel expressed as semi-axis lengths, so GATB forms them from the edge lengths:

\[a = \frac{\left|\mathbf{P}_3 - \mathbf{P}_2\right|}{2}, \qquad b = \frac{\left|\mathbf{P}_1 - \mathbf{P}_2\right|}{2}\]

NOTE: The panel's third semi-axis — its thickness — is not derived from the HVE surface. It is set to a fixed 2 inches for every panel. A contact surface whose real thickness differs substantially from that will behave accordingly in the ATB contact model.

The lap belt contact ellipsoid¶

ATB applies a lap belt against a contact ellipsoid, and HVE's human carries no such ellipsoid. Where a lap belt is in use, GATB synthesizes one from the segments either side of it: the two transverse semi-axes are taken from the abdomen ellipsoid, and the vertical semi-axis is twice that of the pelvis ellipsoid:

\[a = a_{Abdomen}, \qquad b = b_{Abdomen}, \qquad c = 2\,c_{Pelvis}\]

It is centred on the pelvis ellipsoid, offset downward by the pelvis semi-axis:

\[z = z_{Pelvis} - c_{Pelvis}\]

The result is a single ellipsoid spanning the abdomen and pelvis, which is what the lap belt bears against. It exists only for the belt calculation and is not part of the human's own contact geometry.

Integration timestep¶

GATB always writes a fixed ATB integration timestep of 0.002 sec, and the number of steps is the maximum simulation time divided by it. Within each step, ATB's own variable-step Runge-Kutta/predictor-corrector integrator controls the solution.

For the underlying theory of the ATB model — the equations of motion, joint models, contact force model and restraint (harness and airbag) models — see the four-volume CVS/ATB documentation and the ATB-V.1 documentation listed in Chapter 7, Technical References.

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